The age of the car is the most significant factor when determining importation eligibility for a non-USDM (US Domestic Market) vehicle.
Any car that is 25 years or older can be registered as a classic and can forgo all of the rigorous federal safety and emissions standards newer cars would require. Though your state may still have some standards that they require the car to comply with. Essentially all you will have to do is find the car you want to buy, have it brought to a port, ship it, and register it once it arrives. Obviously this is an enormous simplification of the process. Make sure to have an experienced importer helping you to make sure the proper vehicle is purchased and all the paperwork is filled out correctly, you will not be able to do the paperwork yourself. With a little common sense importing a 25 year old car is definitely possible.
Cars less than 25 years old are much more involved. The car will have to be brought into compliance with the DOT safety regulations and if it is less than 21 years old it will also have to be made compliant with EPA emissions regulations. Bringing the car the car into compliance is extensively more difficult (and expensive) than it sounds. For the car to be considered compliant with the DOT safety regulations you will have to add various US specified safety equipment like airbags, headlights, crash beams, etc. This will cost a few thousand dollars depending on the car. But the government still won’t know that the car’s new safety features are up to par, so you will then have to do what manufacturers do and crash test it. And not just once. If your features don’t work properly you will have to do it again. And there are multiple crash tests that need to done so even if you have all of the correct features you will still need extra (modified) cars to perform the other tests on. This testing will cost a few hundred thousand dollars. Emissions testing will also need to be done but the cost and the work involved are microscopic compared to the safety testing. As you can imagine the cost and effort involved is too voluminous for most people.
But there are two other options. One for the average person and one for the better than average person. If you are better than average buying a better than average car you may qualify for the “Show and Display” clause. The car will need to have less than 500 models produced, will only be permitted to drive 2500 miles a year, but can be brought to the United States without any alterations whatsoever. The average person option is called the “Substantially Similar” clause. Vehicles deemed by the manufacturer or by the government to be substantially similar to a vehicle approved for the US can be imported albeit with a few changes. This clause is primarily intended for Canadians bringing their cars to the US (the two countries have strikingly similar specifications). A car coming from any other country will struggle to fall under this clause.
So while importing a foreign spec car is possible it’s out of the reach of most people. There have been companies that have completed the crash testing and sold the cars in the US but depending on what kind of car you wanted they may or may not still be around. And they keep their secrets heavily guarded. If you are looking for a European or Japanese car your best option is to just wait until it’s 25 years old and the rules are much easier to comply with.